The resistance and propulsion of ships

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ARCHIEF

WILLIAM F. DURAND:

,,THE RESISTANCE AND

PROPULSION OF SHIPS"

2ND EDITION I 909.

tab.

v.

ScheepsbouwtcunJe

Techniscte Hog eschool

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WILLIAM F. DURAND:

,,The Resistance and Propulsion of Ships."

2ND EDITION 1909.

The principal equations which we have to use:

Let w denote wake factor

prismatic, or cylindrical coefficient;

/3 ,, midship-section coefficient; L ,,

length in feet

p ,, - pitch ,, N Number of revolutiOnS.

p1N1)' d

kim;. p1

_''100'

d 10'

pN

l0I.3,u

_1s1

= (I ± w)

(I-(1:-

w) .1

-

=

(fLt/6

- .6) for single screw-ships;

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1 '.13

(jL76

- 1.1) for twin-screw ships;

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The values of k,. l,m, e2, and of 101.3 u may be taken from

Tables I, H, Ill,

IV, V for the values of slip, pitch-ratio,

area-ratio, and speed given, and b interpolationfor intermediatevalues.

Table I. Values of Factor k.

SL1P-RATI0.. k SLIP-RATIO. k ' SLIP-RATIO. k

.10 . A10 '.22' - .168: .32 .195 .12 .121 .24 .175 .34 .199 .14 . .132 ' .26 . .181 .36 .202 .16

:,

.142 .28 .186

'.38

.204 .18 ;151 .30 .191 ' .40 .205

'.20

.160.'

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Table II. Values:of Factor 1.

PITCH-RATIO: SLIP-RATIO. 1.5 1.6 . 1.7 L8 . - 1.9 2.0 .524

.465

..412.

368

.329 . .293 .12 .539 .481 430 384 .345 .311 .14 .550 . .493 .441 .397- - .359 - .325 .16 .560 .503 .452 .408 .369 ..336 .18 .569 .512. 46'1 .417

379..

- .345

20 :

-. 577 .521 .. .469 .426 .386 ..

352

-.22, .24 -.584 . .590 - .528 . .478 .536

' 44

.434 .441 .394 .401 .360 .366 .26 596 :542

_{:,..491 .... 448:.}

.. -'.406 .372 .28 : .600 .547 .496 454 .412 . .377 .30 .605 .551 - , .501 .458 .417 .381 .32 .609 .555. - .505. .462 .421 '- .385

'34

.612 .558 .509

:.466

.424 .389 .36 .614 .560. .512 .469 ' - :428 .392 38 615 562 514 471 430 - 394 .4Y

.16

.563 .515 .472

-432

-.396

SLIP-RATIO. .8 .9 .1.0 1.2 J.3 1.4 .10 1.35 1.15 1.00 .871 .763 .675 .594 .12 132 1.14 1.00 .875 .771 .682 -.610 .14 1.30 1.13 1.00 .879 .778 .691 .621 .16 1.29 1.13 1.00 .883 .784 .700 .630 .18 1.28 1.12 1.00- .886 .790 .707 .637 .20 1.28 1.12 1.00 - .889 .795 .714 .644 .22 1.28 1.12, 1.00. .891 .799 .719 .649 .24 1.28 1.1-2 1.0L -.89, .802 .724 .655 .26 1.28 1.12 1.00 .895 .806 727 .660 .28 1.27 1.12 1.00

.897.

.809 .731. .664

30

1.27 1.12 1.00 .899 .812 .734 .668 .32 1.27 1.12 1.00 .900 .816 .737 .670 .34 1.27 1.12 1.00 :. .818 .739 .673 .36 1.27 1.12 1.00 . .902 .81,9 .741

65

.38 1.27 1.12 1.00 .903 .820 .742 .676 .40 1.26 1.12 1.00 .903 - 820 .742 .676

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Table 111

Values of Factor m.

PITCH-RATIO .8. PiTCH-RATIO .9. PITCH-RATIO 1:1. SLIP-RATIO. - AREA-RATIO.

20

.30 .40 .50 .60 .1.0 ..595 .852 .1.00 1.07 1.12 20 715 895

1.0

1.05 1.08

:30

755 .919 1.00 1.04 1.07 40 .-784

.930 -

1.00 1.04 1.06 PITCH1RATIO 1:2. SLIP-RATIO. AREA-RATIO..

.201.30

.40

.60.

.10 .20 .575

:go

.843.890 1.00

.i.00

L08

I.06 . 1.13 1.09 -' .743 .912 I 00 105 1.07 .770 .925 1.00 1.04 1.07 AREA-RATIO. SLIP-RATIO. .20 .30 .40 .50 .60 :10 .660 883 i.00 1.06 1. .09 .2O .750 914 1.00 1.04 1.07 .30 .793 .930 1.00 1.03 1.05 .40 .820 .944. 1.00 1.02 1.03 PITCH-RATIO 1.0. SLIP-RATIO. AREA-RATIO

.20.

.30 .40 .50 .60 .10 .620 865 1.00 I

r.io

.20 :725 .905 1.00 1.05 07 .30 .773 .927 1.00 1.04 1.06 .40 .802 .940 1.00 1.03 1.05 AREA-RATIO. SLIP-RATIO. .20 .30 .40 .50 .60 .10 .730 .900 I .00 .05 1.07 .20 .783 .927 1.00 1.04 1.06 .30 .819 .942 1.00 1.03 1.04. .40 .840 .950 1. .00 1.02 1.02

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PITCH-RATIO 1. AREA-RATIO. .20 .30 .40 .50 .60 .541 .813 1.00 1.10 1.15 .669

£73

1.00 1.07 1..I I .715 .892 1.00 1.06 1.09 .730 .902

i.00

1.06 1.09 PITCH-RATIO 1.7. AREA-RATIO.

..20

.30 .40 .50 .60

.540.

.812 1.00

110

1.15

.68

.873 1.00 1.07 1 .712 .895 LOU 1.06 1.09 .724 .901 LOU 1.06 1.09 PITCH-RATIO L3. AREA-RATIO. .20 .30 .40 .50 .60 .560 .831 1.00. ..i.09. 1.14 .680 .880 1.00 1.06 .11Q .732 .905 1.00 LOS 1.08 .755 919 1.00 1.05 1.08 PITCH-RATIO 1.4. AREA-RATIO. .20 .30 .40 .50 .60 .552 .823 i.oö

I.09

1.14 .674

£80

1.00 1.06 1.10 .726 .903 1.00 1.06 1.09 .744 .913 I 00 1.05 1.08 PiTCH-RATIO 1.5. AREA-RATIO .20 .30 .60 .549 .818 LOU 1.10 1.15 .670 .875 1.00 1.07

1.10

.720 .899 1.00 1.06 1.09 .736 .908 1.00 1.05 I .09

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PiTCH-RATIO 1.8. AREA-RATIO. SLIP-RATIO. .20 .30 .40 .50 .60 .10 .540 .813 1.00 1.10 1.16 .20 .669 .872 1.00 1.07 1.11 .30 .710 .892 1.00 1.06 1.10 .40 .719 .899 1.00 1.06 1.09 PITCH-RATIO 1.9. AREA-RATIO. SLIP-RATIO. .20 .30 .40 .50 .60 .10 .549 .815 1.00 1.11 1.16 .20 .670 .873 1.00 1.07 1.11 .30 .710 .891 1.00 -1.06 1.10 .40 .719 .899 1.00 1.06 1.09 PITCH-RATiO 2.0. AREA-RATIO. SLIP-RATIO. .20 .30 .40 .50 .60 .10 .556 .819 1.00 1.11 1.16 .20 .674 .873 1.00 1.07 1.12 .30 .711 .891 1.00 1.06 1.10 .40 .718 .899 1.00 1.06 1.09

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.10 .20 .30 .40 SLIP-RATIO. .10 .20 .30 40 SLIP-RATIO. ..Io .20 30 .40 SLIP-RATIO. .10 .20 .30 .40

Table IV. Values of Efficiency.

PITCH-RATIO .8.. AREA-RATIO. .20 .30 .40 .0 .60 .58 6 I .63 '.63. .63 .64 .65 .66. . .66 .66 .62 .62 .63 .63 .63 .58 .58 .58 .58 .58 PITCH-RATIO .9. AREA-RATIO :20 . .30 .40 .50 .60 .57 .61 .64 .64 .63 .66 .67 .67 .67 .66 .64 .6 .64 .64 .64 .60 .59 .59' .58 .58 PITCH-RATIO .1.0. AREA-RATIO .30 .40 .30' .60" .57 .61 .64 .64 64 .67 :68 68 .68 '.67 .66 .66 .65 .64 .63,. .62 .61 .60 .58 .58 PITCH-RATIO 1.1. AREA-RATIO. .20 3Ø . .40 .50 .60 .56 .61 .64 .65 .65 .69 .69 .69 .68 .68 .68 .67 .66 .65 .64 .64 .62 .60 .5g 58 PITCH-RATIO 1.2. AREA-RATIO .20 .30 .40 .50 .60 .56 .61 .64 .65' .64' 70 .70 .69 .69 .69 .70 .68 .68 .66 .65 .65 63 .62 .60 39

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PITCH-RATIOT L3. PITCH-RATIO 1.7. 7. SLIP-RATIO. AREA-RATIO. .20 .30 .40 .50 .60 .10 . 54 ' .60 .64 .65 .66 .20 ' .72 .72 .72 .71 .70 .30 .72 .72 .71 .69 .68 .40 .68 .67 .65 .64 .63 SUP-RATIO. AREA-RATIO. .20 . .30 40 .50 .60

;i0

: 61 .64 .65 .65 .20 71 ;71 .70 :".70 .69 3O :71

.70.

.69 67 .65 ?40 .66 .65 .64 .61' 60 PITCH-RATIO' 1.4. SLIP-RATIO. 'AREA-RATIO. 20 .30 .40 .50 .60

.IO

:52 F ...60 ....63 .64. .64 .20 71 .

'.73

.73.

.72 .72 .30 '.72 .73 72 .71 .70 :40 .68 .68 .67 65 .65

PITCH-RArIO 1.5.

SLIP-RATIO.

AR-RATIO

.20

'.30

.40 .50 .60

y10

.60 .64 .65 .66 .71 .72 ..71 .70 .70 :30 :.72 .71 .69 .68 .66 .40 .67 .65 .64 .62 .61 PITCH-RATIO 1.6. SLIP-RATIO. AREA-RA'fIO. .20 F .30 40 , .50 .60

.10

.54 .60 .64 .65 .66 .20 .72 .72

12

.71 .70 .30 .73 .72 .70 .68 .68 .40 .68 .66' .64 .63 .62

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8 PITC I-I-RATIO 1.8. AREA-RATIO. SLIP-RATIO. .20 !30 .40 .50 .60 '.10 .53 .60 .64 .65 .65 .20 .72 .73 .73 .72 .71 .30 .73 .73 .71 .70 .69 AU .69 .67 66 .64 PITCH-RATIO 1.9. SLIP-RATIO. AREA-RATIO. .20 .30

'..40

. .50 60 .10 .53 .60 .63 .65 .65 .20 .72 .73 '73, .72 .71 .30 .72 .73

12

.70

70

.40 .69 .68 .66 .65 '.64 PITCH-RATIO ZO. AREA-RATIO SLIR-RATlO. 20 .30 .40 .50

.60

-1O

.52.

.60 .63 .64 .64 20 .71 .74 73 .72 .71 30 .72 .73 .72 .71. .70 .40 .68 .68 ' .67 .66 :65

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Table V.

Giving Feet per Mm.

corresponding To Knots.

Or Values of 101,3 u.

9 u 101,3u. u 101,3u. 10 1013 25 2533

II

1115 26 2635 12 1216 27 2736 13 1317 28 2837 14 1419 29 2939 15 1520 30 3040 16 1621 31 3141 V 17 1723 V 32 3243 18 1824 33 3344 19 1925 34 3445 20 2027 35 3547 21 2128 36 3648 22 2229 37 3749. 23 2331 38 3851 24 2432 39 V 3952